Practice Questions

Duration: 2 min

This video lesson is available to enrolled students.

Return to /learn/COAL-INDIA-MANAGEMENT-TRAINEE/engineering-maths/propositional-and-predicate-logic/practice-problems-on-quantifiers-and-predicate-logic/asset-practice-questions-2397 after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Paper-2 | Programming & Data Structures: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  3. Paper-2 | Databases / DBMS & SQL: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control
  4. Paper-2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  5. Paper-2 | Computer Networks & Security: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware Basics, Network Access Technologies, Network Security
  6. Paper-2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  7. Paper-2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  8. Paper-2 | Theory of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines
  9. Paper-2 | Computer Organization & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer
  10. Paper-2 | Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  11. Paper-1 | General Awareness: Polity, Physics, Biology, Chemistry, Static General Knowledge, GK- Current Affairs, History, Geography, Indian Economy, Environment
  12. Paper-1 | Logical Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Data Interpretation, Blood Relations, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Clock, Calendar, Cubes & Dices, Directions (Direction Test), Analogy, Seating Arrangements, Analytical Reasoning (Counting Figures Reasoning)
  13. Paper-1 | Quantitative Aptitude: Ratio and Proportion (Ratios), Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Speed Time and Distance, Average, Age Problems, Percentage, Profit and Loss, Time and Work, Pipe and Cistern, Simple Interest and Compound Interest, Powers and Exponents (Surds and Indices), Mensuration and Geometry, Probability, Statistics, Arithmetic, Algebra
  14. Paper-1 | English: Vocabulary, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Cloze Test (Cloze Passage)
  15. Coal India Previous Year Paper:
  16. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus
  17. Coal India Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video segment demonstrates the process of finding the negation of a logical statement involving quantifiers and logical connectives. The instructor presents a specific problem involving existential ($\exists$) and universal ($ orall$) quantifiers combined with implication ($

ightarrow$) and disjunction ($\vee$). The core task is to apply logical rules to transform the original statement into its negation. The visual aid includes the full mathematical expression written in orange text at the top of the screen.

Chapters

  1. 0:00 – 1:50 00:00-01:50

    The video opens with the question displayed at the top: 'negation of the statement $\exists_x orall_y [F(x, y) ightarrow \{G(x, y) \vee H(x, y)\}]$'. The instructor underlines the left and right sides of the equation to highlight the components. He begins writing the solution by placing a negation symbol ($\sim$) before the entire expression. He then systematically flips the quantifiers, changing the existential quantifier $\exists_x$ to a universal quantifier $ orall_x$ and the universal quantifier $ orall_y$ to an existential quantifier $\exists_y$. Next, he addresses the negation of the implication $F(x, y) ightarrow \{G(x, y) \vee H(x, y)\}$. He explains that the negation of an implication $P ightarrow Q$ is equivalent to $P \wedge eg Q$. Consequently, the antecedent $F(x, y)$ remains unchanged, while the consequent is negated. He applies De Morgan's Law to the negated disjunction $ eg \{G(x, y) \vee H(x, y)\}$, transforming it into $ eg G(x, y) \wedge eg H(x, y)$. The final written result on the screen is $ orall_x \exists_y [F(x, y) \wedge \{ eg G(x, y) \wedge eg H(x, y)\}]$, which matches the right side of the original equation shown.

The lesson effectively breaks down a complex logical negation problem into manageable steps. By first handling the quantifiers and then focusing on the propositional logic within the brackets, the instructor clarifies the transformation process. The key takeaway is the rule for negating implications and the application of De Morgan's laws to disjunctions. The final derived statement confirms the logical equivalence presented in the problem statement, reinforcing the student's understanding of quantifier negation rules. This methodical approach ensures that students can follow the logical flow from the initial problem to the final solution without confusion.

Loading lesson…